Achromatic optical system including diffractive optical element

ABSTRACT

An aromatic optical system that preferably includes a light source for emitting light therefrom, an achromatic optical element positioned to receive light emitted from the light source, and an optical detector positioned to receive and detect light passing through the optical element. The achromatic optical element preferably includes a substrate having opposing sides, a first computer generated hologram positioned on one side of the substrate and adapted to receive light emitted from the light source, and a second computer generated hologram positionally aligned on the opposite side of the substrate and adapted to receive light passing through the substrate from the first hologram at a predetermined location thereon. A method of forming an achromatic diffractive optical element is also provided which includes the steps of determining a first data set comprising a plurality of discrete phase values and discrete transition values and selecting from the first data set phase values and transition values to form a second data set for defining first and second holograms. A discrete value of the second data set is then replaced by another discrete value from the first data set. A change of an optical system error function is then determined responsive to the replacement in the second data set. If the error function is reduced, the new data set is retained.

FIELD OF THE INVENTION

This invention relates to holography, and more particularly to opticalsystems and holographic lenses, also referred to as diffractive opticalelements, and holographic fabrication methods.

BACKGROUND OF THE INVENTION

Developments in diffractive optics technology have opened the doors fordiffractive optical elements ("DOEs") to play major roles in a widenumber of optical systems and applications including high resolutionimaging systems such as head-mounted displays, focussing and collimatingoptics for fiber-optic couplers and connectors and other opticalinterconnect applications, and chromatic aberration correction ofrefractive optical elements.

One type of diffractive optical element known as a "natural hologram" isfabricated by creating interference among coherent light beams on aphotographic plate and then developing the photographic plate. Anexample of such a hologram may be seen in U.S. Pat. No. 4,607,914 byFienup titled "Optical System Design Techniques Using HolographicOptical Element." These natural holograms, however, are difficult tomass produce.

In order to overcome the mass production problems with interferometricholograms, computer generated holograms ("CGHs") have been developed.CGHs have been fabricated by calculating the desired holographic patternto perform a particular function and then forming the pattern on a glassor other substrate using photolithographic or other techniques. Thistechnique is described, for example, in U.S. Pat. No. 4,960,311 by Mosset al. titled "Holographic Exposure System For Computer GeneratedHolograms."

When natural holograms are used to replace conventional refractiveoptical elements such as lenses and prisms, they are typically referredto as holographic optical elements ("HOEs"). In order to distinguishHOEs from CGHs when CGHs are used to replace similar refractiveelements, they are typically referred to as diffractive optical elements("DOEs").

While natural holograms are conventionally analog in nature, CGHs on theother hand are conventionally digital in nature. That is the calculationof the CGH is often done by calculating a CGH pattern at discretelocations often referred to as "pixels" and quantizing phase and/oramplitude functions to discrete levels. This is done principally tosimplify the fabrication of CGHs. For example, in U.S. Pat. No.4,895,790 by Swanson et al. titled "High-Efficiency, Multilevel,Diffractive Optical Elements," a method is described for fabricatingCGHs containing 2^(N) phase levels, where N is the number of masks andetching steps employed.

DOEs, however, can also be fabricated by a continuous method, forexample by diamond turning the calculated pattern onto a glasssubstrate. DOEs fabricated in this manner are often termed continuousDOEs, while DOEs fabricated with discrete steps are typically termed,"binary optics," "multilevel DOEs", or "digital optics."

A well known problem associated with DOEs is a large amount of chromaticaberrations. For example, while a single DOE can be designed to yielddiffraction limited performance for imaging or focussing a singlewavelength, the DOE exhibits severe chromatic aberrations, much largerthan that of a comparable refractive imaging/focusing lens, whenwavelengths other than the design wavelength are employed.

This is especially important when a broadband light source, such as anLED, is used (e.g., for imaging, collimating, or focussing) with a DOE.It is also important, however, when a very narrow band light source suchas a laser diode is employed. This is because the lasing wavelength oflaser diodes typically has a very high sensitivity to temperature, e.g.,0.30-0.5 nanometers per degree centigrade (°C.). In addition, manyfiber-optic connectors are designed to operate with several differenttypes of laser diodes, each having a different wavelength.

While it is known that a refractive optical element can be combined witha DOE to perform achromatic imaging, it is much more difficult toachieve achromatic imaging with solely diffractive elements. Due totheir low cost, it is often desirable to manufacture DOEs with solelydiffractive surfaces, especially in large volumes.

It is also known that two DOEs can be analytically designed or designedwith computer ray tracing procedures so that they function together toreduce chromatic aberrations. For example, in a publication titled"Wavelength Independent Grating Lens System," Applied Optics, Vol. 28,No. 4, pp. 682-686, 1989, by Kato et al., a method was described havingtwo distinct DOEs in a complimentary manner so that two differentwavelengths could be brought to a common focal point. A ray tracingprocedure is described in which two holograms are used to image a pointon-axis. The spatial frequency at each point along the radius (r) ofeach DOE is calculated so that rays for two different wavelengths arebrought to a common focus. The DOE is then fabricated with a gratingperiod that varies as a function of r. The period of the grating as afunction of r is determined by the spatial frequencies calculated duringthe ray tracing procedure.

This particular technique, however, has several drawbacks. First, thediffraction efficiency of this technique is severely limited. Thegratings employed are binary gratings. Binary phase gratings have anefficiency of about 40% for a combined efficiency of about 16% fortransmission through both DOEs.

The number of levels that can be employed with such a technique islimited by the minimum feature size of such processes. The maximumnumber of phase levels (N) that can be employed in such a process isgiven by:

    N≦T/δ                                         (1)

where delta (δ) is the minimum feature size. The diffraction efficiency(η) in the +1 order of a grating with N phase levels is given byEquation (2) set forth below: ##EQU1##

If the grating period needed is 2 micrometers (μm) and the minimumfeature size is 0.5 μm, then the maximum number of phase levels that canbe employed is 4, yielding an efficiency of each DOE of about 80% andcombined efficiency of about 64%. Note that this limitation stems from adesign procedure that considers only a single diffraction orderemanating from each grating (the +1 order), when in actuality, for amultilevel DOE, multiple orders are actually generated.

This limitation is a drawback of ray tracing and continuous analytictechniques. That is, the DOE surfaces are modelled as continuousfunctions or continuous blazed gratings. Such continuousfunctions/gratings generate only a +1 order with 100% efficiency (intheory). In practice, a multilevel DOE is not continuous. The discretesteps are responsible for generating multiple diffraction orders,lowering the efficiency in the +1 diffraction order.

A second drawback of this approach is that the two optical elements mustbe placed relatively far apart to minimize the spatial frequenciescontained in the elements. The maximum deflection angle that can berealized with reasonable diffraction efficiency with state-of-the-artfabrication techniques is approximately 25 degrees (°). Assuming asource divergence half angle of 15° and equal sized elements, thislimits the distance (D) of separation between the two DOEs to greaterthan about three times the diameter (d) of each of the elements. In manycases, it is desirable to place the elements closer together to improvealignability or reduce the overall system volume.

A third drawback is that this approach is not a diffraction basedapproach, but instead a geometrical optics based approach. Thus, whileit can be used to minimize or eliminate geometrical aberrations, it willnot in most cases achieve diffraction limited performance. That is theoptimization procedure will result in perfect geometrical opticsperformance for two different wavelengths, but no diffraction effectsare accounted for in this procedure. Thus, the tailoring of the sidelobes of the DOE and other diffraction based effects cannot be performedwith this procedure. Thus, for example, it could not be used directly tooptimize the coupling efficiency for a laser-to-fiber coupler or tocreate a flat-top profile.

Fourth, this method is limited to radially symmetric DOEs. This is adrawback for use with many commercial diode lasers that containdifferent divergence angles in the two orthogonal directions. For suchasymmetrical cases, it is often desirable to have non-radially symmetricanamorphic lenses.

Finally, with this method, the resulting DOEs are generally notidentical to each other. In some cases, as in separable fiber-opticcouplers, it is desirable to have the two DOEs identical so that theparts can be interchangeable as with conventional fiber-optic separableconnectors.

Another method that is known for designing DOEs is iterative encodingmethods such as iterative discrete on-axis ("IDO") encoding described inthe publication titled "Iterative Encoding Of High-Efficiency HologramsFor Generation Of Spot Arrays," Optical Society of America, pp. 479-81,1989, by co-inventor Feldman et al., and radially symmetric iterativediscrete on-axis ("RSIDO") encoding described in U.S. Pat. No. 5,202,775titled "Radially Symmetric Hologram And Method Of Fabricating The Same"also by co-inventor Feldman et al.

In the IDO encoding method, the DOE is divided into a two-dimensionalarray of rectangular cells. An initial transmittance value for eachrectangular cell is chosen. An iterative optimization process, such assimulated annealing, is then used to optimize the transmittance valuesof the cells. This is achieved by choosing an error function for thehologram that is a measure of the image quality. A single cell ischanged, and the change in the output pattern is computed. The errorfunction is then recalculated. Based upon the change in the errorfunction, the change is either accepted or rejected. The process isiteratively repeated until an acceptable value of the error function isreached which optimizes the image quality. Computers are often used forperforming these iterations because of the immense time involved in theoptical system calculations.

The RSIDO encoding method is another iterative method, except that thecells are radial rings rather than rectangular and not only are thephase values of each cell optimized, but also the transition points.Although this method has been shown to be successful for variousapplications, the amount of chromatic compensation that can be achievedwith this method, however, may be limited.

Another known method for designing DOEs for achromatic operation, suchas described in the publications titled "Deep Three-dimensionalMicrostructure Fabrication For IR Binary Optics," J. Vac. Sci. Technol.B10, pp. 2520-2525, 1992 by Stern et al. and titled "Dry Etching: PathTo Coherent Refractive Microlens Arrays," SPIE Proc., pp. 283-292, 1992,is to create deep multilevel DOEs that have phase depths that are largerthan conventional multilevel DOEs. In conventional digital optics, thephase depth (d_(m)) of each level is given by ##EQU2## where n is theindex of refraction and m=0, 1, . . . N-1 and λ is the centralwavelength. This will result in a phase difference between the m=0 leveland any other level of 2π m/N.

In a deep multilevel DOE, on the other hand, the phase difference is setequal to an integer number multiple of 2π (m/N) (e.g., 4π m/N or 6πm/N). It is known that d_(m) can be set equal to any integer multiple of2π and the DOE will not function any differently. Within predeterminedparaxial approximations at the design wavelength, however, the chromaticaberrations about this wavelength will improve.

A problem with this approach is that the diffraction efficiency is lessthan that of the conventional DOE approach. Instead of Equation 2, thediffraction efficiency for the deep multilevel approach is: ##EQU3##where p is the integer multiple of 2π employed. Thus, for example if thephase difference were set to 8πm/N, p would have a value of 4, and foran 8 phase level structure, the diffraction efficiency of a deepmultilevel DOE would be only 40% as compared to 95% for an 8 phase levelconventional multilevel DOE.

In practice, the above approaches have resulted in reasonable efficiencyDOEs with only a small amount of chromatic aberration for practicalapplications. For example, for laser diode-to-fiber couplers, a couplingefficiency of greater than 70% was achievable with a single wavelength.Over an operating temperature range of -40° to +85° C., however, lessthan about 5% may be achieved with a single DOE designed with commercialray tracing programs. By using a single element RSIDO encoded hologram,the coupling efficiency was improved to about 15%-17% over the operatingtemperature range. The other methods described above may not bepractical for this application due to one or more of the followingreasons: low efficiency, high cost, or large volume.

Thus, there is a continued need for achromatic optical systems andachromatic DOEs with high diffraction efficiency for various practicalcommercial applications.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide an opticalsystem and a diffractive optical element ("DOE") that have highdiffraction efficiency over a wide spectral range.

It is also an object of the present invention to provide a method offabricating a hologram that is practical in terms of cost and size, suchas for laser diode and LED applications and for head-mounted displayapplications.

These and other objects are provided, according to the presentinvention, by an achromatic optical system having a light source foremitting light therefrom, an achromatic diffractive optical elementpositioned to receive light emitted from the light source, and anoptical detector positioned to receive and detect light passing throughthe optical element. The achromatic optical element preferably includesa substrate having opposing sides, a first hologram positioned on oneside of the substrate and adapted to receive light emitted from thelight source, and a second hologram positioned on the opposite side ofthe substrate and adapted to receive light passing through the substratefrom the first hologram at a predetermined location thereon.

The first hologram is preferably a computer generated hologrampositioned on one side of the substrate and preferably has a firstmultilevel diffractive surface. The first computer generated hologram isadapted to receive light emitted from the light source and pass thereceived light through the first multilevel diffractive surface. Thesecond hologram is also preferably a computer generated hologrampositionally aligned on the opposite side of the substrate and alsopreferably has a second multilevel diffractive surface. The secondcomputer generated hologram is adapted to receive light passing throughthe substrate from the first hologram at a predetermined location on thesecond multilevel surface.

An achromatic diffractive optical element according to the presentinvention advantageously provides only diffractive surfaces withachromatic performance over a wide wavelength range. The achromaticdiffractive optical element also has significantly higher diffractionefficiency than could be achieved with previous methods.

The present invention also includes methods of forming and designing anachromatic diffractive optical element. These methods preferably havethe steps of determining a first data set comprising a plurality ofdiscrete phase values and discrete transition values. From the firstdata set, phase values and transition values are selected to form asecond data set for defining the first and second holograms. A discretevalue of the second data set is preferably replaced by another discretevalue from the first data set, and a change of an optical system errorfunction is determined responsive to the replacement in the second dataset. The new data set is then retained if the error function is reduced.The steps of replacing a discrete value of the second data set,determining a change of an optical system error function, and retainingthe new data set if the error function is reduced is repeated until atleast one of the values has been replaced at least one time to therebyoptimize the discrete phase values and the discrete transition values.The first hologram and the second hologram are then fabricated from theoptimized discrete phase values and discrete transition values ontorespective opposing sides of a substrate using techniques such asdeposition and lift-off.

The methods of designing and fabricating an achromatic diffractiveoptical element according to the present invention differ from previousdual element diffractive achromatic structures in at least two majorrespects. First, with these methods, the diffractive surfaces aremodelled as discrete surfaces with quantized phase values. Second,diffraction theory, instead of ray tracing, is used to determine thecomplex amplitude distribution in the output plane in order to calculatethe error function on each iteration. Thus, unlike previous achromaticDOE design approaches, the achromatic diffractive optical elementaccording to the present invention can be designed to optimize fordiffraction effects. Therefore, the efficiency of the achromaticdiffractive optical element is not limited to the product of theefficiencies of the individual hologram surfaces given by Equations (2)and (4) set forth above. Since wave diffraction is used in the designrather than ray tracing, the achromatic diffractive optical element canbe optimized to take advantage of multiple diffraction orders of the twohologram surfaces. Equations (2) and (4) above, for example, give thepower in the +1 order only.

Furthermore, by use of appropriate cell or fringe sizes, restrictions onmaximum spatial frequencies in the holograms are automatically includedthereby allowing the holograms to be placed closer together than withprevious ray tracing methods. Diffraction efficiency is also improvedwith the use of an iterative procedure such as the IDO or RSIDO encodingmethods. Additionally, a restriction that the two holograms have thesame transmittance function can also be included, and the two elementsdo not need to be radially symmetric.

With these diffractive optical element design methods, since discretelevel iterative encoding methods are employed, "phase skipping" may alsooccur. Phase skipping means that the phase difference between some ofthe fringes is greater than 1 phase level, but less than N-1 levels.Phase skipping provides an advantage in that the optical element can bedesigned and fabricated to achieve improved diffraction efficiency.

BRIEF DESCRIPTION OF DRAWINGS

Some of the objects and advantages of the present invention having beenstated, others will become apparent as the description proceeds whentaken in conjunction with the accompanying drawings in which:

FIG. 1 is a schematic view of an achromatic optical system according tothe present invention illustrating at least first and second wavelengthsof light being transmitted through an achromatic diffractive opticalelement;

FIG. 2 is a schematic view of an achromatic optical system according toa first embodiment of the resent invention;

FIG. 3 is a schematic view of an achromatic optical system according toa first embodiment of the present invention and further illustratingfiber optic lines in the system;

FIG. 4 is a schematic view of an achromatic optical system according toa second embodiment of the present invention;

FIG. 5 is a schematic view of an achromatic optical system according toa third embodiment of the present invention;

FIG. 6 is an enlarged schematic view of an achromatic diffractiveoptical element according to the present invention;

FIG. 7 is an enlarged schematic view of portions of a hologram of anachromatic diffractive optical element according to a first embodimentof the present invention;

FIG. 8A is an enlarged schematic view of portions of a hologram of anachromatic diffractive optical element according to a second embodimentof the present invention;

FIG. 8B is an enlarged schematic view of portions of a hologram of anachromatic diffractive optical element according to a second embodimentof the present invention;

FIG. 9 is an enlarged schematic view of a hologram of an achromaticdiffractive optical element according to a second embodiment of thepresent invention;

FIG. 10 is a block diagram that illustrates a method of designing andfabricating an achromatic diffractive optical element according thepresent invention; and

FIG. 11 is a table comparing the diffraction efficiencies of diffractiveoptical elements designed by a ray tracing method versus diffractiveoptical elements designed by a method according to the presentinvention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

The present invention now will be described more fully hereinafter withreference to the accompanying drawings in which preferred embodiments ofthe invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theillustrated embodiments set forth herein; rather, the embodiments areprovided so that this disclosure will be thorough and complete and willfully convey the scope of the invention to those skilled in the art. Forclarity, the thickness of layers have been exaggerated. Like numbersrefer to like elements throughout.

FIG. 1 is a schematic view of an achromatic optical system 20 accordingto the present invention. The optical system 20 preferably has a lightsource 25, shown in the form of a laser diode, for emitting light Ltherefrom, an achromatic diffractive optical element 40 positioned toreceive light L emitted from the light source 25, and an opticaldetector 30 positioned to receive and detect light L passing through theoptical element 40. The achromatic diffractive optical element 40preferably includes a substrate 41 having opposing sides 41a, 41b, afirst hologram 43, preferably a computer generated hologram ("CGH"),positioned on one side 41a of the substrate 41 and adapted to receivelight L emitted from the light source 25, and a second hologram 45,preferably a CGH, positioned on the opposite side 41b of the substrate41 and positionally aligned with the first hologram 43. The secondhologram 45 is adapted to receive light L which passes through thesubstrate 41 from the first hologram 43 at a predetermined locationthereon.

FIG. 1 further illustrates a first wavelength λ₁ of light L from thelight source 25 being transmitted through the achromatic diffractiveoptical element 40 with a first shading pattern and a second wavelengthλ₂ from the light source 25 being transmitted through the achromaticdiffractive optical element 40 with a second shading pattern. This viewillustrates that different wavelengths illuminate different portions ofthe second hologram 45 so that different functions in the secondhologram 45 may be advantageously used in these different portions.Regions of overlap of the wavelengths are illustrated with a thirdshading pattern, and regions where neither wavelength is present areshown with no shading pattern.

In some applications of the optical system 20, such as wavelengthdivision multiplexing ("WDM"), multiple lasers or laser diodes may beemployed, each with a narrow spectral width of light emission and largespacing between the bands, e.g., 1560.6, 1557.5, 1554.2, 1551, and 1480nanometer (nm) with each one ±0.5 nm, to thereby form a series of bands.A WDM multiplexer coupler then receives light from each laser andcouples all of the light from the lasers into a single fiber optic. AWDM demultiplexer then receives the light from the fiber optic andtransfers each wavelength into a different fiber or different detector.This optical system 20 illustrates that the diffractive optical element45 of the present invention may be designed for such discrete bands ofwavelengths.

FIGS. 2-5 schematically illustrate other embodiments of an achromaticoptical system 20, 20' according to the present invention. For clarity,like elements in these embodiments are referred to by prime (') ordouble-prime (") notation. FIG. 2 is a schematic view of an achromaticoptical system 20 according to a first embodiment of the presentinvention similar to that shown in FIG. 1. The broken lines and arrowsshown from the light source 25, through the diffractive optical element45, and to the detector 30 illustrate the travel of wavelengths of lightL. FIG. 3 is a schematic view of an achromatic optical system 20according to a first embodiment of the present invention, but alsohaving a pair of elongate fiber optic lines, cables, or strands 26, 31which are preferably respectively connected to the light source 25 andthe detector 30.

FIG. 4 is a schematic view of an achromatic optical system 20' accordingto a second embodiment of the present invention. This embodiment of theoptical system 20' illustrates a pair of fiber optic couplers 27', 32'connected to each respective fiber optic line 26', 31'. Each coupler27', 32' has a respective hologram 43', 45' which is positioned on aseparate substrate 41a', 41b' within the coupler 27', 32'. The couplers27', 32' preferably are coaxially positioned and align when joined so asto form a diffractive optical element 40' according to the presentinvention.

FIG. 5 is a schematic view of an achromatic optical system 20" accordingto a third embodiment of the present invention. This embodimentillustrates a large spectral width light source 25", such as a lightemitting diode ("LED"), positioned within the optical system 20". Thelight L emitted from the LED 25" passes through an achromatic opticalelement 40", to a fiber optic line 31", and then preferably to adetector 30 such as illustrated in other embodiments.

FIGS. 6-9 schematically illustrate achromatic diffractive opticalelements according to various embodiments of the present invention. Anachromatic diffractive optical element according to the presentinvention may also be called a dual diffractive achromatic ("DDA")optical element. FIG. 6 is an enlarged schematic view of an achromaticdiffractive optical element 40 according to the present invention. Thisview illustrates the respective multilevel surfaces 43a, 45a of each ofthe first hologram 43 and the second hologram 45, as well as thepositioning of the holograms 43, 45 on a substrate 41.

FIG. 7 schematically illustrates a hologram 43, 45 of an achromaticdiffractive optical element 40 according to a first embodiment of thepresent invention and designed by a radially symmetric iterativediscrete on-axis ("RSIDO") encoding method. The RSIDO encoding method isfurther described in U.S. Pat. No. 5,202,775 by co-inventor Feldmantitled "Radially Symmetric Hologram And Method Of Fabricating The Same"which is hereby incorporated herein in its entirety by reference.

FIGS. 8A and 8B are enlarged schematic views of portions of a hologram43', 45' of an achromatic diffractive optical element 40' according to asecond embodiment of the present invention. These holograms 43', 45'preferably are designed by a method called segmented radial portions("SRP"), The hologram 43', 45' is segmented into regions, i.e., tworegions illustrated in FIG. 8B. Within each region, a RSIDO encodingmethod is utilized so that fringes are portions of circles or arcs. Thetransition values or points, e.g., each radius, are located so as tominimize an error function for many values of theta (θ), which is acoordinate in a hologram plane. This same method may also be used toapproximate elliptically shaped fringes. In addition, instead of usingradial fringes as a model for each holographic surface, rectangularpixels may also be used for methods of designing and fabricating anachromatic diffractive optical element according to the presentinvention.

FIG. 9 schematically illustrates a hologram 43", 45" of an achromaticdiffractive optical element 40" according to a third embodiment of thepresent invention. This embodiment preferably is designed by a methodcalled generalized RSIDO. This method of designing a hologram uses theRSIDO method, but instead of finding one radius (r) per fringe, severalradii for each fringe are located. Each radius located has a differentvalue of θ. Interpolation is then performed with a smooth curve or asegmented polygon to form a contour that connects all of the radii.

FIG. 10 is a block diagram 70 that illustrates a method of designing andfabricating an achromatic diffractive optical element 40 according tothe present invention. As shown in block 71 a desired optical system isfirst specified. In this step, the designer determines the performancecharacteristics for the optical system 20. These performancecharacteristics may vary depending on the application. For example, thedesigner may want to use the achromatic diffractive optical element fora head-mounted display. If this is the desired application, then thedesigner specifies the desired optical system performance to achieve thedesired results as will be understood by those skilled in the art.

Afterwards, as shown in block 72, the optical system parameters areidentified. For example, once the desired optical system has beenspecified, the designer may identify a set of optical parameters for thegiven system by performing geometric, radiometric, or scalar diffractivecalculations well known to those skilled in the art. These opticalsystem parameters may include the curvature of a hologram, therefractive index of a hologram, location and size of a hologram, animage point, focal length, the size of an image, relative spacingbetween optical elements if more than one is included in the system, thewavelength of the light source 25, as well as other parametersunderstood by those skilled in the art.

The next step, as shown in block 73, is to determine the optical systemconstants. The optical system constants, well known to those skilled inthe art, may be determined by utilizing the identified set of opticalsystem parameters. For example, an f-number of a hologram is normallydetermined by the focal length of the hologram divided by the diameterof that hologram. Both the element focal length and element diameter areinitial optical system parameters identified in block 72. Once thef-number is calculated, it will remain the same or constant throughoutvarious changes to improve the imaging performance of the specifiedoptical system.

As shown in block 74, a plurality of phase transition values or pointsand phase values between the transition points are determined for eachfringe of the first and second holograms based on the identified set ofoptical system parameters in block 72 and the optical system constantsin block 73. The transition points are preferably radial phasetransition points, and the phase values are likewise preferably radialphase values for each fringe. In order to determine the initialplurality of radial phase transition points and radial phase values, twomethods may be employed. The first is to randomly choose the values. Thesecond method is to use conventional ray tracing or analytic methods,such as described in the publication titled "Wavelength IndependentGrating Lens System," Applied Optics, Vol. 28, No. 4, pp. 682-686, 1989,by Kato et al. which is hereby incorporated herein by reference in itsentirety, to determine the initial values. A transmittance function foreach of the two different hologram surfaces are determined by dividingeach surface into a set of pixels. The pixels may be rectangular cellsor circular or elliptically shaped fringes as described above withreference to FIGS. 7-9.

Next, as shown in block 75, the diffraction pattern on the secondhologram surface is calculated preferably with the Rayleigh-Sommerfelddiffraction formula. The scalar amplitude and phase distribution on thesecond hologram surface is given by, ##EQU4## where U(P₂) is the scalaramplitude and phase distribution in the plane of the first surface ofthe first hologram and the integrals are evaluated over the entire firsthologram surface plane (ds). The scalar amplitude and phase distributionare found by multiplying the incident wave A(r21) by the firsttransmittance function, H(P2), of the first hologram surface.

    U(P.sub.2)=H(P.sub.2)A(r.sub.21)                           (6)

The diffraction pattern in the output plane is also calculatedpreferably by applying the Rayleigh-Sommerfeld diffraction formula againto obtain: ##EQU5## where U(P1) is the scalar amplitude and phasedistribution on the exit side of the second hologram surface. The scalaramplitude and phase distribution U(P1) are given by:

    U(P.sub.1)=H.sub.2 (P.sub.1)A(P.sub.1)                     (8)

In this manner the output pattern of the achromatic diffractive opticalelement 40, U(P0), is computed.

This equation may also be digitized and then used to compute thepercentage of power located within a given area which represents thepower incident on a detector or coupled into a fiber. This can then beused as the basis for determining an error function as shown in block76.

Other performance characteristics may also be used related to a measureof image quality for the error function. The phase transmittance of thecells and the transition location of the fringes are preferablydetermined by iterative optimization. As shown in blocks 77, 78, 78a,and 78b, the transmittance function of both hologram surfaces is changedon each iteration and thereby optimized.

For example, a single cell may be changed on the first hologram surface,and the diffraction pattern on the second hologram surface is updated.Then the change in the output pattern is determined. The error functionis then recalculated. Based upon the change in the error function, thechange is either accepted or rejected. The process is iterativelyrepeated until an acceptable value of the error function is reachedwhich optimizes the image quality.

In addition, the structure of the DDA element is different thandiffractive elements generated with continuous or ray tracingapproaches. With continuous, ray tracing approaches, when the element isactually fabricated, it is often fabricated as a multilevel DOE. Inorder to generate a multilevel DOE with this method and still have thedesign valid (i.e., Equation (2) for the efficiency), another method,such as described in U.S. Pat. No. 4,895,790 by Swanson et al. must beapplied. In this method a particular number of phase levels, N, ischosen based on the minimum feature size (δ) and smallest grating periodaccording to the Equation set forth below. ##EQU6## The phase levels areevenly divided according to equation (3). The number of phase levelsbetween any two adjacent fringes (regions of constant phase) is equal toone (1), except between fringes where the difference is equal to thenumber of phase levels minus one (N-1).

As shown in block 79 of FIG. 10, once the final radial phase values andradial phase transition values are obtained, the DDA optical element canbe fabricated with multiple masks and etching or deposition steps.Alternatively, it can also be fabricated by direct write with a laser orelectron-beam.

An etch depth can be chosen according to Equation (3) as in conventionalmultilevel hologram surfaces, or by an integer multiple of d_(m) givenin Equation (3) for deep multilevel DOEs. The use of deep multilevelhologram surfaces in DDA optical element configuration would provideadditional achromatic advantages. These deep multilevel DDA opticalelements may be fabricated with or without phase skipping. Althoughglass and quartz, due to their transparent nature, are the most commonmaterials for fabrication of diffractive optical elements, siliconwafers can be used for wavelengths longer than about 1.0 μm. Forwavelengths less than about 1.0 μm, though, the absorptive properties ofsilicon are usually too large for usefulness.

Hydrogenated amorphous silicon, however, can be used to change theabsorption edge of silicon, thereby reducing the percentage of lightabsorbed by the silicon by up to several orders of magnitude in thewavelength range between about 0.73 μm and about 1.0 μm. Even lowerwavelengths may be achieved by sputtering alloys of amorphous silicon orpolysilicon such as Si--Ge or Si--O2. Hydrogenated amorphous silicon canbe deposited by sputtering or by glow discharge chemical vapordeposition. A hologram surface can be fabricated by adeposition/lift-off technique, or by depositing a thin film of amorphoussilicon and etching the film with a conventional chemical or dry etchingtechnique.

Since substrates of such materials are not available in wafer form, aconventional transparent diffractive optical element substrate, such asquartz or a type of glass, may be employed. These substrates have alower refractive index, i.e., about 1.4 to 1.5, and thus would requirean intermediate layer to act as an anti-reflection coating between theglass substrate and the silicon film.

Further, according to the present invention,. a method of aligning twoor more holograms is also provided. In the preferred embodiment, the twoholograms are fabricated on opposite sides of a single substrate. Thefirst hologram is fabricated on one side of the substrate, and in theconventional manner, each layer of the hologram is aligned to a singleset of alignment marks. In addition, however, as this first hologram isfabricated, a third hologram is also formed with the sole purpose offacilitating alignment with the second hologram. This third "alignmenthologram" is designed to form an alignment pattern on the second side ofthe substrate when illuminated by a laser beam at normal incidence.

After forming the first hologram on the first side of the substrate, thesecond side of the substrate is coated with photoresist. A laser is thenused to illuminate the "alignment hologram" on the first side of thesubstrate and to expose the photoresist on the second side of thesubstrate. After photoresist development, an alignment mark is formed onthe second side of the substrate that is well-aligned to the first sideof the substrate, e.g., within about 0.5 μm.

FIG. 11 is a table comparing the diffraction efficiencies of samples ofdiffractive optical elements designed by a ray tracing method versussamples of achromatic diffractive optical elements designed by themethod of the present invention. The diffractive optical elements areused to couple light from one fiber optic line to another fiber opticline, such as illustrated in embodiments of the optical systems of FIGS.8 and 9. The goal in these examples was to couple light over a 100 nmbandwidth, i.e., 1250 nm to 1350 nm. The diameter of each hologram ofthe optical element was about 125 μm and the spacing between elementswas about 1.0 mm.

The data from the table shows the unexpected results achieved by themethod of designing an achromatic diffractive optical element accordingto the present invention wherein the resulting diffractive opticalelement has a significant improvement in diffraction efficiency, as wellas other performance characteristics, in comparison to other designmethods.

In the drawings and specification, there have been disclosed typicalpreferred embodiments of the invention, and although specific terms areemployed, they are used in a descriptive sense only and not for thepurposes of limitation. The invention has been described in considerabledetail with specific reference to various preferred embodiments. It willbe apparent, however, that various modifications and changes can be madewithin the spirit and scope of the invention as described in theforegoing specification and defined in the appended claims.

That which is claimed is:
 1. A diffractive optical element comprising:a transmissive computer generated hologram formed of hydrogenated amorphous silicon and having a diffractive surface, said computer generated hologram being adapted to receive light emitted from a light source having a wavelength less than 1.0 micrometer and to pass the received light through said diffractive surface.
 2. A diffractive optical element as defined by claim 1, wherein said hologram is fabricated by deposition and lift-off.
 3. A diffractive optical element comprising:a computer generated hologram having a multilevel diffractive surface including more than two levels, said computer generated hologram being adapted to receive light emitted from a light source and to pass the received light through said multilevel diffractive surface, said hologram having phase skipping and having phase level differences which are larger than 2π.
 4. A diffractive optical element as defined by claim 1 wherein said diffractive surface includes more than two levels.
 5. A diffractive optical element as defined by claim 3 wherein said computer generated hologram is formed of hydrogenated amorphous silicon. 